Gradient corrections to the kinetic energy density functional of a two-dimensional Fermi gas at finite temperature

Abstract

We examine the leading-order semiclassical gradient corrections to the noninteracting kinetic-energy density functional of a two-dimensional Fermi gas by applying the extended Thomas-Fermi theory at finite temperature. We find a nonzero von Weizs\"acker-like gradient correction, which in the high-temperature limit goes over to the functional form $(\ensuremath{\hbar}{}^{2}/24m)(\ensuremath{\nabla}\ensuremath{\rho}){}^{2}/\ensuremath{\rho}$. Our work provides a theoretical justification for the inclusion of gradient corrections in applications of density-functional theory to inhomogeneous two-dimensional Fermi systems at any finite temperature.